Spectral Analysis of Bounded Self-adjoint operators - A Linear Algebraic Approach

This thesis Entitled Spectral theory of bounded self-adjoint operators -A linear algebraic approach.The main results of the thesis can be classified as three different approaches to the spectral approximation problems. The truncation method and its perturbed versions are part of the classical linear algebraic approach to the subject. The usage of block Toeplitz-Laurent operators and the matrix valued symbols is considered as a particular example where the linear algebraic techniques are effective in simplifying problems in inverse spectral theory. The abstract approach to the spectral approximation problems via pre-conditioners and Korovkin-type theorems is an attempt to make the computations involved, well conditioned. However, in all these approaches, linear algebra comes as the central object. The objective of this study is to discuss the linear algebraic techniques in the spectral theory of bounded self-adjoint operators on a separable Hilbert space. The usage of truncation method in approximating the bounds of essential spectrum and the discrete spectral values outside these bounds is well known. The spectral gap prediction and related results was proved in the second chapter. The discrete versions of Borg-type theorems, proved in the third chapter, partly overlap with some known results in operator theory. The pure linear algebraic approach is the main novelty of the results proved here.

Synthesis, Spectral and Structural Studies of a Novel Semicarbazone Synthesized from Quinoline-2-Carboxaldehyde and N4-Phenyl-3-Semicarbazide

A new semicarbazone, HL has been synthesized from quinoline-2-carboxaldehyde and N4-phenyl-3- semicarbazide and structurally and spectrochemically characterized. 1H NMR, 13C NMR, IR and electronic spectra of the compound are studied. The existence of keto form in the solid state is supported by the crystal structure and IR data. The compound crystallizes into an orthorhombic space group P212121. Intra and intermolecular hydrogen bonding interactions facilitates unit cell packing in the crystal lattice

Synthesis, spectral and structural studies of oxovanadium(IV/V) complexes derived from 2-hydroxyacetophenone-3-hydroxy- 2-naphthoylhydrazone: polymorphs of oxovanadium(V) complex [VOL(OCH3)]

Oxovanadium(IV/V) complexes of 2-hydroxyacetophenone- 3-hydroxy-2-naphthoylhydrazone (H2L) have been synthesized and characterized. The complexes were characterized by elemental analyses, IR, electronic and EPR spectra. The oxovanadium(V) complex [VOL (OCH3)] is crystallized in two polymorphic forms, denoted by 1a and 1b, with space groups Pn21a and P 1, respectively. Both have distorted square pyramidal structures.

Synthesis, spectral characterization and crystal structure of copper(II) complexes of 2-benzoylpyridine-N(4)-phenylsemicarbazone

An interesting series of nine new copper(II) complexes [Cu2L2(OAc)2] H2O (1), [CuLNCS] ½H2O (2), [CuLNO3] ½H2O (3), [Cu(HL)Cl2] H2O (4), [Cu2(HL)2(SO4)2] 4H2O (5), [CuLClO4] ½H2O (6), [CuLBr] 2H2O (7), [CuL2] H2O (8) and [CuLN3] CH3OH (9) of 2-benzoylpyridine-N(4)-phenyl semicarbazone (HL) have been synthesized and physico-chemically characterized. The tridentate character of the semicarbazone is inferred from IR spectra. Based on the EPR studies, spin Hamiltonian and bonding parameters have been calculated. The g values, calculated for all the complexes in frozen DMF, indicate the presence of the unpaired electron in the dx2 y2 orbital. The structure of the compound, [Cu2L2(OAc)2] (1a) has been resolved using single crystal X-ray diffraction studies. The crystal structure revealed monoclinic space group P21/n. The coordination geometry about the copper(II) in 1a is distorted square pyramidal with one pyridine nitrogen atom, the imino nitrogen, enolate oxygen and acetate oxygen in the basal plane, an acetate oxygen form adjacent moiety occupies the apical position, serving as a bridge to form a centrosymmetric dimeric structure

Syntheses, EPR spectral studies and crystal structures of manganese(II) complexes of neutral N,N donor bidentate Schiff bases and azide/thiocyanate as coligand

Four manganese(II) complexes Mn2(paa)2(N3)4 (1), [Mn(paa)2(NCS)2] 3/2H2O (2), Mn(papea)2(NCS)2 (3), [Mn(dpka)2(NCS)2] 1/2H2O(4) of three neutral N,N donor bidentate Schiff bases were synthesized and physico- chemically characterized by means of partial elemental analyses, electronic, infrared and EPR spectral studies. Compounds 3 and 4 were obtained as single crystals suitable for X-ray diffraction. Compound 4 recrystallized as Mn(dpka)2(NCS)2. Both the compounds crystallized in the monoclinic space groups P21 for 3 and C2/c for 4. Manganese(II) is found to be in a distorted octahedral geometry in both the monomeric complexes with thiocyanate anion as a terminal ligand coordinating through the nitrogen atom. EPR spectra in DMF solutions at 77 K show hyperfine sextets with low intensity forbidden lines lying between each of the two main hyperfine lines and the zero field splitting parameters (D and E) were calculated.

Structural, Spectral, Biological and Electrochemical Studies Of Some 3d Transition Metal Complexes of O-N-S and N-N-S Donor Ligands

The primary aim of these investigations was to probe the spectroscopic, electrochemical, biological and single crystal X-ray diffraction studies of some selected transition metal complexes of 4N-monosubstituted thiosemicarbazones. Transition metal complexes with thiosemicarbazones exhibit a wide range of stereochemistries and possess potential biological activity. Metal complexes of thiosemicarbazones are proved to have improved pharmacological and therapeutic effects. The studies are conducted to bring about a fair understanding of the structure activity relationship and to develop certain effective and economical metal-based antimicrobial agents. Study showed that the thiosemicarbazones have antibacterial, antiviral and antiproliferative properties and hence used against tuberculosis, leprosy, psoriasis, rheumatism, trypanosomiasis and coccidiosis. Certain thiosemicarbazones showed a selective inhibition of HSV and HIV infections. The insolubility of most thiosemicarbazones in water causes difficulty in the oral administration in clinical practice. Transition metal complexes are found to have more activity than uncombined thiosemicarbazones. They exhibit a variety of denticity and can be varied by proper substitution. The stereochemistry assumed by the thiosemicarbazones during the coordination with transition metal ions depends on the factors such as preparative conditions and availability of additional bonding site in the ligand moiety and charge of the ligand. The resulting complexes exhibited a wide range of stereochemistries and have biomimic activity and potential application as sensors.

Synthesis, Spectral Characterization, Structural Studies and Biological Investigations of Transition Metal Complexes of Some Acid Hydrazones

This study concentrates the chemical properties of hydrazones due to its chelating capability and their pharmacological applications. Studies cover the preparation of different acid hydrazones and their structural studies and studies on their antimicrobial activity, synthesis and spectral characterization of different complexes of copper oxovanadium, manganese, nickel etc. Effect of incorporation of heterocyclic bases to the coordination sphere, change in the biological activity of acid hydrazones upon coordination, development of X-ray quality single crystals and its X-ray diffraction studies, studies on the redox behavior of the coordinated metal ions and correlation between the stereochemistry and biological activities.

Spectral Characteristics of the Blood of Streptozotocin Diabetic Rats using Photoacoustic Technique

Optical absorption characteristics of rat blood affected by diabetes has been studied using photoacoustic (PA) technique. PA spectrum of blood depends on the molecular structure of haemoglobin. The peak value ratio ylQ increases with increase in the diabetic state. Externally added glucose to normal blood does not show any increase in y//3 ratio as seen in the diabetic condition . The increase in yl,8 ratio may be due to the decrease in DPG level and the resultant shift from R -> T conformation of majority of diabetic haemoglobin.

Structural and Spectral Investigations of Transition Metal Complexes Of Di-2-Pyridyl Ketone N (4), N (4)-Disubstituted Thiosemicarbazones

The study deals with structural and spectral investigations of transition metal complexes of di-2-pyridyl ketone N(4),N(4)-disubstituted thiosemicarbazones. The main objective and scope of the work deals with di-2-pyridyl ketone N(4),N(4)-disubstituted thiosemicarbazones are quardridentate NNNS donor ligands. To chosen this ligand for study because, the ligands are prepared and characterized for the first time, since there are two pyridyl nitorgens, dimmers and polymers of complexes may result leading to interesting structural aspects. The work includes the preparation of the thiosemicarbzones and their structural and spectral studies, synthesis and spectral characterization of complexes of copper(II),,nickel(II),manganese(II), dioxovanadium(V),cobalt(III),zinc(II),cadmium(II) of the ligand HL, synthesis and spectral characterization of complexes of copper(II),manganese(II), of the ligand HL and the development of X-ray quality crystals and its X-ray diffraction studies. The structural characterization techniques are elemental analysis, conductivity measurements, magnetic measurements, electronic spectroscopy, H NMR spectroscopy, Infrared spectroscopy and X-ray crystallography.

Structural, Spectral, Biological and Electrochemical Studies Of Some 3d Transition Metal Complexes of O-N-S and N-N-S Donor Ligands

The primary aim of these investigations was to probe the spectroscopic, electrochemical, biological and single crystal X-ray diffraction studies of some selected transition metal complexes of 4N-monosubstituted thiosemicarbazones. Transition metal complexes with thiosemicarbazones exhibit a wide range of stereochemistries and possess potential biological activity. Metal complexes of thiosemicarbazones are proved to have improved pharmacological and therapeutic effects. The studies are conducted to bring about a fair understanding of the structure activity relationship and to develop certain effective and economical metal-based antimicrobial agents. Study showed that the thiosemicarbazones have antibacterial, antiviral and antiproliferative properties and hence used against tuberculosis, leprosy, psoriasis, rheumatism, trypanosomiasis and coccidiosis. Certain thiosemicarbazones showed a selective inhibition of HSV and HIV infections. The insolubility of most thiosemicarbazones in water causes difficulty in the oral administration in clinical practice. Transition metal complexes are found to have more activity than uncombined thiosemicarbazones. They exhibit a variety of denticity and can be varied by proper substitution. The stereochemistry assumed by the thiosemicarbazones during the coordination with transition metal ions depends on the factors such as preparative conditions and availability of additional bonding site in the ligand moiety and charge of the ligand. The resulting complexes exhibited a wide range of stereochemistries and have biomimic activity and potential application as sensors